A Machine Learning interview calls for a rigorous interview process where the candidates are judged on various aspects such as technical and programming skills, knowledge of methods and clarity of basic concepts. If you aspire to apply for machine learning jobs, it is crucial to know what kind of interview questions generally recruiters and hiring managers may ask. This is an attempt to help you crack the machine learning interviews at major product based companies and start-ups. Usually, machine learning interviews at major companies require a thorough knowledge of data structures and algorithms. In the upcoming series of articles, we shall start from the basics of concepts and build upon these concepts to solve major interview questions. Machine learning interviews comprise of many rounds, which begin with a screening test. This comprises solving questions either on the white-board, or solving it on online platforms like HackerRank, LeetCode etc. Here, we have compiled a list of ...

The current work is motivated by the need for robust statistical methods for precision medicine; as such, we address the need for statistical methods that provide actionable inference for a single unit at any point in time. We aim to learn an optimal, unknown choice of the controlled components of the design in order to optimize the expected outcome; with that, we adapt the randomization mechanism for future time-point experiments based on the data collected on the individual over time. Our results demonstrate that one can learn the optimal rule based on a single sample, and thereby adjust the design at any point t with valid inference for the mean target parameter. This work provides several contributions to the field of statistical precision medicine. First, we define a general class of averages of conditional causal parameters defined by the current context for the single unit time-series data. We define a nonparametric model for the probability distribution of the time-series under few assumptions, and aim to fully utilize the sequential randomization in the estimation procedure via the double robust structure of the efficient influence curve of the proposed target parameter. We present multiple exploration-exploitation strategies for assigning treatment, and methods for estimating the optimal rule. Lastly, we present the study of the data-adaptive inference on the mean under the optimal treatment rule, where the target parameter adapts over time in response to the observed context of the individual. Our target parameter is pathwise differentiable with an efficient influence function that is doubly robust - which makes it easier to estimate than previously proposed variations. We characterize the limit distribution of our estimator under a Donsker condition expressed in terms of a notion of bracketing entropy adapted to martingale settings.

This paper studies the problem of recovering the hidden vertex correspondence between two edge-correlated random graphs. We focus on the Gaussian model where the two graphs are complete graphs with correlated Gaussian weights and the Erd\H{o}s-R\'enyi model where the two graphs are subsampled from a common parent Erd\H{o}s-R\'enyi graph $\mathcal{G}(n,p)$. For dense graphs with $p=n^{-o(1)}$, we prove that there exists a sharp threshold, above which one can correctly match all but a vanishing fraction of vertices and below which correctly matching any positive fraction is impossible, a phenomenon known as the "all-or-nothing" phase transition. Even more strikingly, in the Gaussian setting, above the threshold all vertices can be exactly matched with high probability. In contrast, for sparse Erd\H{o}s-R\'enyi graphs with $p=n^{-\Theta(1)}$, we show that the all-or-nothing phenomenon no longer holds and we determine the thresholds up to a constant factor. Along the way, we also derive the sharp threshold for exact recovery, sharpening the existing results in Erd\H{o}s-R\'enyi graphs. The proof of the negative results builds upon a tight characterization of the mutual information based on the truncated second-moment computation and an "area theorem" that relates the mutual information to the integral of the reconstruction error. The positive results follows from a tight analysis of the maximum likelihood estimator that takes into account the cycle structure of the induced permutation on the edges.

We consider the question of sequential prediction under the log-loss in terms of cumulative regret. Namely, given a hypothesis class of distributions, learner sequentially predicts the (distribution of the) next letter in sequence and its performance is compared to the baseline of the best constant predictor from the hypothesis class. The well-specified case corresponds to an additional assumption that the data-generating distribution belongs to the hypothesis class as well. Here we present results in the more general misspecified case. Due to special properties of the log-loss, the same problem arises in the context of competitive-optimality in density estimation, and model selection. For the $d$-dimensional Gaussian location hypothesis class, we show that cumulative regrets in the well-specified and misspecified cases asymptotically coincide. In other words, we provide an $o(1)$ characterization of the distribution-free (or PAC) regret in this case -- the first such result as far as we know. We recall that the worst-case (or individual-sequence) regret in this case is larger by an additive constant ${d\over 2} + o(1)$. Surprisingly, neither the traditional Bayesian estimators, nor the Shtarkov's normalized maximum likelihood achieve the PAC regret and our estimator requires special "robustification" against heavy-tailed data. In addition, we show two general results for misspecified regret: the existence and uniqueness of the optimal estimator, and the bound sandwiching the misspecified regret between well-specified regrets with (asymptotically) close hypotheses classes.

We present counterfactual planning as a design approach for creating a range of safety mechanisms that can be applied in hypothetical future AI systems which have Artificial General Intelligence. The key step in counterfactual planning is to use an AGI machine learning system to construct a counterfactual world model, designed to be different from the real world the system is in. A counterfactual planning agent determines the action that best maximizes expected utility in this counterfactual planning world, and then performs the same action in the real world. We use counterfactual planning to construct an AGI agent emergency stop button, and a safety interlock that will automatically stop the agent before it undergoes an intelligence explosion. We also construct an agent with an input terminal that can be used by humans to iteratively improve the agent's reward function, where the incentive for the agent to manipulate this improvement process is suppressed. As an example of counterfactual planning in a non-agent AGI system, we construct a counterfactual oracle. As a design approach, counterfactual planning is built around the use of a graphical notation for defining mathematical counterfactuals. This two-diagram notation also provides a compact and readable language for reasoning about the complex types of self-referencing and indirect representation which are typically present inside machine learning agents.

After challenging the validity of these assumptions in real-world applications, we propose ways to move forward when they are violated. First, we show that group fairness criteria purely based on statistical properties of observed data are fundamentally limited. Revisiting this limitation from a causal viewpoint we develop a more versatile conceptual framework, causal fairness criteria, and first algorithms to achieve them. We also provide tools to analyze how sensitive a believed-to-be causally fair algorithm is to misspecifications of the causal graph. Second, we overcome the assumption that sensitive data is readily available in practice. To this end we devise protocols based on secure multi-party computation to train, validate, and contest fair decision algorithms without requiring users to disclose their sensitive data or decision makers to disclose their models. Finally, we also accommodate the fact that outcome labels are often only observed when a certain decision has been made. We suggest a paradigm shift away from training predictive models towards directly learning decisions to relax the traditional assumption that labels can always be recorded. The main contribution of this thesis is the development of theoretically substantiated and practically feasible methods to move research on fair machine learning closer to real-world applications.

In this paper, we study the information theoretic bounds for exact recovery in sub-hypergraph models for community detection. We define a general model called the $m-$uniform sub-hypergraph stochastic block model ($m-$ShSBM). Under the $m-$ShSBM, we use Fano's inequality to identify the region of model parameters where any algorithm fails to exactly recover the planted communities with a large probability. We also identify the region where a Maximum Likelihood Estimation (MLE) algorithm succeeds to exactly recover the communities with high probability. Our bounds are tight and pertain to the community detection problems in various models such as the planted hypergraph stochastic block model, the planted densest sub-hypergraph model, and the planted multipartite hypergraph model.

Theoretical results show that Bayesian methods can achieve lower bounds on regret for online logistic regression. In practice, however, such techniques may not be feasible especially for very large feature sets. Various approximations that, for huge sparse feature sets, diminish the theoretical advantages, must be used. Often, they apply stochastic gradient methods with hyper-parameters that must be tuned on some surrogate loss, defeating theoretical advantages of Bayesian methods. The surrogate loss, defined to approximate the mixture, requires techniques as Monte Carlo sampling, increasing computations per example. We propose low complexity analytical approximations for sparse online logistic and probit regressions. Unlike variational inference and other methods, our methods use analytical closed forms, substantially lowering computations. Unlike dense solutions, as Gaussian Mixtures, our methods allow for sparse problems with huge feature sets without increasing complexity. With the analytical closed forms, there is also no need for applying stochastic gradient methods on surrogate losses, and for tuning and balancing learning and regularization hyper-parameters. Empirical results top the performance of the more computationally involved methods. Like such methods, our methods still reveal per feature and per example uncertainty measures.

Perfect adaptation in a dynamical system is the phenomenon that one or more variables have an initial transient response to a persistent change in an external stimulus but revert to their original value as the system converges to equilibrium. The causal ordering algorithm can be used to construct an equilibrium causal ordering graph that represents causal relations and a Markov ordering graph that implies conditional independences from a set of equilibrium equations. Based on this, we formulate sufficient graphical conditions to identify perfect adaptation from a set of first-order differential equations. Furthermore, we give sufficient conditions to test for the presence of perfect adaptation in experimental equilibrium data. We apply our ideas to a simple model for a protein signalling pathway and test its predictions both in simulations and on real-world protein expression data. We demonstrate that perfect adaptation in this model can explain why the presence and orientation of edges in the output of causal discovery algorithms does not always appear to agree with the direction of edges in biological consensus networks.

Artificial Intelligence (AI), and in particular, the explainability thereof, has gained phenomenal attention over the last few years. Whilst we usually do not question the decision-making process of these systems in situations where only the outcome is of interest, we do however pay close attention when these systems are applied in areas where the decisions directly influence the lives of humans. It is especially noisy and uncertain observations close to the decision boundary which results in predictions which cannot necessarily be explained that may foster mistrust among end-users. This drew attention to AI methods for which the outcomes can be explained. Bayesian networks are probabilistic graphical models that can be used as a tool to manage uncertainty. The probabilistic framework of a Bayesian network allows for explainability in the model, reasoning and evidence. The use of these methods is mostly ad hoc and not as well organised as explainability methods in the wider AI research field. As such, we introduce a taxonomy of explainability in Bayesian networks. We extend the existing categorisation of explainability in the model, reasoning or evidence to include explanation of decisions. The explanations obtained from the explainability methods are illustrated by means of a simple medical diagnostic scenario. The taxonomy introduced in this paper has the potential not only to encourage end-users to efficiently communicate outcomes obtained, but also support their understanding of how and, more importantly, why certain predictions were made.